In this section we test the capabilities of a neural network that takes as input the Laplace-Beltrami eigenfunctions to perform a regression task on a manifold. In this case, we do not include any physics that may act as a regularization of the predicted function. For this benchmark, we compare against Gaussian process regression with a Matérn kernel, which can be approximated on the manifold using the Laplace-Beltrami eigenfunctions as well [1]}. We choose a dragon geometry 9,057 vertices and 18,110 triangles. We create a synthetic ground truth function by computing the geodesic distance from a vertex \(d(\mbox{$x$}{})\) :
\(f(\mbox{$x$}{}) = \sin \left(\pi \frac{d(\mbox{$x$}{})}{d_{max}}\right)\) 
